Suppose just 5% of the potential jurors believe, say, that it should not be illegal to kill an abortion doctor, or to beat up someone who dares to be homosexual in public, or to beat up someone who dares to flirt with a white woman while being black, and so on.
If you have a jury of 12 and require a unanimous verdict for conviction, then 46% of randomly chosen juries will not convict people for the aforementioned crimes no matter what the evidence, because they will include at least one person who believes those acts should not be criminal.
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for whomever wondering how tzs comes up with the numbers, he probably models this problem as a binomial distribution, e.g., Bin(12, 0.05). while binomial distribution is a good approximation for this case, i think hypergeometric is better, since it's not 5% anymore as soon as you choose one juror.
No distribution needed - 46% is 100% - (100% - 5%)^12, as if you were rolling a die 12 times. The population is large enough that the effect of removing 11 people from it should be negligible.
This is not "no distribution", this is a binomial distribution - where every one of n items has an equal probability p of being a certain result. You are correct that in this case removing the 11 people from the population is negligible, thus p remains the same.
If you have a jury of 12 and require a unanimous verdict for conviction, then 46% of randomly chosen juries will not convict people for the aforementioned crimes no matter what the evidence, because they will include at least one person who believes those acts should not be criminal.
<rant>
for whomever wondering how tzs comes up with the numbers, he probably models this problem as a binomial distribution, e.g., Bin(12, 0.05). while binomial distribution is a good approximation for this case, i think hypergeometric is better, since it's not 5% anymore as soon as you choose one juror.
</rant>